Explanation

Compound adjective is formed when two or more words are combined to describe a noun, like "five-star" in this case.

It modifies the noun "hotel," describing the quality or rating of the services offered.

Explanation

First, let's find the work rate of 10 men:

10 men construct 75 km in 5 days, so:

Work rate = 75 km / 5 days = 15 km/day for 10 men

Now, let's find the work rate for 15 men:

Work rate for 15 men = (15/10) × 15 km/day = 22.5 km/day

Now, let's find the time needed for 15 men to construct 45 km:

Time = Distance / Work rate

= 45 km / 22.5 km/day

= 2 days

Explanation

We know the identity:

a³ - b³ = (a - b)(a² + ab + b²)

Here, 8x³ - 27y³ = (2x)³ - (3y)³

= (2x - 3y)((2x)² + (2x)(3y) + (3y)²)

Given 2x - 3y = 8 and xy = 2:

(2x)² + (2x)(3y) + (3y)² = 4x² + 6xy + 9y²

= 4x² + 6(2) + 9y²

= 4x² + 12 + 9y²

We need to express 4x² + 9y² in terms of 2x - 3y and xy:

(2x - 3y)² = 4x² - 12xy + 9y²

64 = 4x² - 12(2) + 9y²

64 = 4x² - 24 + 9y²

4x² + 9y² = 88

Now, 4x² + 6xy + 9y² = 88 + 12 = 100

So, 8x³ - 27y³ = (2x - 3y)((2x)² + (2x)(3y) + (3y)²)

= 8 × 100

= 800

Explanation

The Halting problem is about determining whether a given program will terminate (halt) or run indefinitely for a specific input.

It was proven by Alan Turing that there is no general algorithm to solve this problem for all possible programs.

Explanation

Over 6000 languages are spoken globally, including many with distinct dialects and regional variations.

This linguistic diversity is mainly concentrated in Asia and Africa, where countries like Papua New Guinea alone have over 800 languages.

Explanation

The formula for the volume of a hemisphere is:

(2/3) × π × r^3

Given diameter = 16.8 cm, so radius (r) = 16.8 / 2 = 8.4 cm

Volume = (2/3) × π × (8.4)^3

= (2/3) × 3.14159 × 592.704

≈ 1241.85 cm^3

Explanation

Under the Indian Councils Act of 1861, the Governor-General of India was empowered to:

• Establish new Legislative Councils in other provinces (e.g., Bengal, NWFP, Punjab).
• Nominate additional members to the Central Legislative Council.

Explanation

Alexander the Great conquered Gandhara in 326–327 BCE during his campaign into the Indian subcontinent.

Gandhara was a key region due to its strategic location and cultural significance.

Explanation

Edge computing involves processing data closer to where it is generated, such as on IoT devices or local servers, reducing latency and bandwidth use.

It enables faster data processing and real-time analytics without needing to send data to a centralized cloud server.

Explanation

"Drop off" refers to the act of taking someone to a specific location and leaving them there.

It's commonly used when someone gives a ride to another person and then leaves them at their destination.